[EM] Clone proofing Copeland

Chris Benham chrisjbenham at optusnet.com.au
Sat Jan 6 13:22:26 PST 2007

Simmons, Forest wrote:

>Here's a version that is both clone proof and monotonic:
>The winner is the alternative A with the smallest number of ballots on which alternatives that beat A pairwise are ranked in first place. [shared first place slots are counted fractionally]
>That's it.
>This method satisfies the Smith Criterion, Monotonicity, and Clone Independence.

More not-so-good news for this  Simmons method: it fails  mono-raise 
(aka Monotonicity).

31: A>B
02: A>C
32: B>C
35: C>A

C>A>B>C. "Simmons" scores:  A35,   B33,   C32.   C has the lowest score 
and wins.

But if we raise C on the two A>C ballots, changing them to C>A, then we get:

31: A>B
32: B>C
37: C>A (2 of these were A>C)

C>A>B>C. "Simmons" scores:  A37,   B31,   C32.  Now  B has  the  lowest  
score  and  wins.

So raising C on some ballots without changing the relative ranking of 
any of the other candidates has
caused C to lose,  a failure of  mono-raise.

Interestingly in both cases the method gave the same result as IRV.  In 
fact it is starting to look as
though in the 3-candidate case "Schwartz//Simmons"  is equivalent to 

Say sincere is:

48: A
27: B>A
25: C>B

B is the CW, and in this case both methods (even without the "Schwartz" 
component) elect B.

And both methods are vulnerable to the same Pushover strategy. If from 3 
to 20 of the 48 A supporters
change their vote to C>A or C or even C>B, then both methods will elect A.

45: A
03: C>A (sincere is A)
27: B>A
25: C>B

B>A>C>B   "Simmons" scores: A27,   B28,  C45.  A has the lowest score 
and so wins.
IRV eliminates B and likewise elects A.

28: A
27: B>A
45: C>B  (20 of these are sincere A!)

B>A>C>B   "Simmons" scores: A27,   B45,  C28.  A has the lowest score 
and so wins.
IRV eliminates B and likewise elects A.

Chris Benham


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